Universities will be told that they must uphold free speech and clamp down on student unions that “no platform” controversial speakers, the government is to announce.

Jo Johnson, the universities minister, set out plans to challenge the culture of so-called safe spaces in universities, which could allow the newly created Office for Students (OfS) to fine, suspend or register universities that fail to protect freedom of speech on campuses.

The proposals will form part of a consultation to help establish how the OfS – which is due to receive its legal powers in April next year – will operate in its regulation of English universities. It will be able to hold them to account over their duty to secure free speech, ensuring it is upheld by staff, student unions and student societies, the Department for Education (DfE) said.

In recent years student unions and campaigners have banned, or attempted to ban, a number of high-profile people from speaking at universities because of their controversial opinions. In one of the most infamous cases, feminist writer Germaine Greer risked being unable to give a lecture after Rachael Melhuish, women’s officer at Cardiff University, called for her to be no-platformed for her “transphobic” views. Greer eventually spoke under tight security.

Nick Lowles, director of Hope Not Hate, LGBT activist Peter Tatchell and Johnson’s brother Boris, the foreign secretary, have faced being barred from speaking. The feminist activist and writer Julie Bindel has been no-platformed by the NUS for several years.

Johnson said that free speech was one of the foundations on which the UK’s higher education tradition was built. “It goes to the heart of our democratic values and is a principle universities hold dear,” he said.

“I know there is good practice out there, and am proud that some of our university leaders and academics have publicly defended free speech. But there are still examples of censorship where groups have sought to stifle those who do not agree with them.”

Earlier in the year the government extended the statutory duty to secure free speech so that it will apply to all providers of higher education registered with the OfS, which was established through the Higher Education Role Analysis scheme.

Johnson said: “I want the OfS to work with universities to encourage a culture of openness and debate and ensure that those with different backgrounds or perspectives can flourish in a higher education environment.”

He told the Times: “Freedom of speech is a fundamentally British value which is undermined by a reluctance of institutions to embrace healthy vigorous debate. Our universities must open minds, not close them.”

Speaking about Greer’s situation, Johnson said it was “preposterous” for her to be banned from speaking in campuses. “She has every right, if invited, to give views on difficult and awkward subjects,” he said. “No-platforming and safe spaces shouldn’t be used to shut down legitimate free speech.

“Our young people and students need to accept the legitimacy of healthy, vigorous debate in which people can disagree with one another. That’s how ideas get tested, prejudices exposed and society advances. Universities mustn’t be places in which free speech is stifled.”

Sir Michael Barber, chair of the OfS, said: “Ensuring freedom of speech and learning how to disagree with diverse opinions and differing views of the world is a fundamental aspect of learning at university. The OfS will promote it vigorously.”